It is difficult to speculate on the exact size because it can expand quite dramatically if he so feels like (e.g., sunny day).
The "mean" or "average" size I would guess to be about 18" to 20". He is not perfectly round but that is more a function of the shape of the rock he is attached to, which is a 30lb piece of shelf rock.
(I bought it special for him.) For a size comparison, the plate coral next to him is roughly between 6" and 7" in diameter. The 90g is obviously 18" front to back and there is a little bit of clearance in the front, but he is mushed up against the back glass. Also in the "left to right" dimension he seems to be more like 20" to 22" (which brings me back to the "not perfectly round" observation).
So I'm afraid a 24x24 cube would probably be just a little too shy for him in the long term. You'd have 1" - 2" of clearance between the anemone and the glass, which will make appropriate flow conditions probably quite challenging, if not impossible.
A 30x30 cube, however, would probably work exceedingly well. In fact, if I don't find him a home that's probably what I will pursue for myself for a species tank for this anemone. In the end, I'm not sure I'm that ready to part with the anemone, but the heartache of losing fish unnecessarily has got to stop, so I have to change things around (one way or the other).
BTW, I refer to him as "he" because he has demonstrated himself to be a male when he spawns (swimmers instead of eggs). When he spawns it makes the tank one very large milky mess for about 24 hours.
Basically you have to really love this anemone, and be OK with having nothing else too exciting along with it. It needs to be a carefully measured choice.